Detection Statistics

Magnitude frequency plot for the UK calculated for the region 10W to 2E and 49N to 59N.

Larger earthquakes occur less frequently than smaller ones. The
relationship is exponential, ie there are ten times as many magnitude
4 or larger earthquakes in a given time period than magnitude 5
or larger earthquakes. This can be expressed by the Gutenberg-Richter
formula

log N = a - b M

where N is the number of earthquakes per year exceeding a given
magnitude M. The constant a reflects the absolute level of seismicity
in an area, and the value of b has generally been found to be
consistently close to 1.0.

The graph shows the relationship for the UK. A least-squares
regression to this data gives the relationship

log N = 3.82 - 1.03 M

Also shown is an alternative doubly-truncated exponential model which
gives a curved fit ot the data at the higher magnitude end.